Tue, 10 Feb 2026
13:00
13:00
L2
Dynamics of the Fermion-Rotor System
Vazha Loladze
(Oxford )
Abstract
In this talk, I will examine the dynamics of the fermion–rotor system, originally introduced by Polchinski as a toy model for monopole–fermion scattering. Despite its simplicity, the system is surprisingly subtle, with ingoing and outgoing fermion fields carrying different quantum numbers. I will show that the rotor acts as a twist operator in the low-energy theory, changing the quantum numbers of excitations that have previously passed through the origin to ensure scattering consistent with all symmetries, thereby resolving the long-standing Unitarity puzzle. I will then discuss generalizations of this setup with multiple rotors and unequal charges, and demonstrate how the system can be viewed as a UV-completion of boundary states for chiral theories, establishing a connection to the proposed resolution of the puzzle using boundary conformal field theory.
Thu, 05 Mar 2026
12:00 -
13:00
C5
Thu, 15 Jan 2026
14:00
14:00
C1
Igusa stacks and the cohomology of Shimura varieties
Pol van Hoften
(Zhejiang University)
Abstract
Associated to a modular form $f$ is a two-dimensional Galois representation whose Frobenius eigenvalues can be expressed in terms of the Fourier coefficients of $f$, using a formula known as the Eichler--Shimura congruence relation. This relation was proved by Eichler--Shimura and Deligne by analyzing the mod p (bad) reduction of the modular curve of level $\Gamma_0(p)$. In this talk, I will discuss joint work with Patrick Daniels, Dongryul Kim and Mingjia Zhang, where we give a new proof of this congruence relation that happens "entirely on the rigid generic fibre". More precisely, we prove a compatibility result between the cohomology of Shimura varieties of abelian type and the Fargues--Scholze semisimple local Langlands correspondence, generalizing the Eichler--Shimura relation of Blasius--Rogawski. Our proof makes crucial use of the Igusa stacks that we construct, generalizing earlier work of Zhang, ourselves, and Kim.
Quantization of the Willmore Energy in Riemannian Manifolds
Michelat, A
Mondino, A
Advances in Mathematics
Thu, 12 Feb 2026
12:00
12:00
Lecture Room 4, Mathematical Institute
Thu, 29 Jan 2026
12:00
12:00
Lecture Room 4, Mathematical Institute
The latent variable proximal point algorithm for variational problems with inequality constraints
John Papadopoulos
Further Information
Abstract
The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. Although equivalent at the continuous level, the saddle point formulation is significantly more robust after discretization.
LVPP yields simple-to-implement numerical methods with robust convergence and observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides; in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge--Ampère equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. Moreover the algorithm is largely discretization agnostic allowing one to discretize with very-high-order $hp$-finite element methods in an efficient manner. In this talk, we will describe the LVPP algorithm in a general form and apply it to a number problems from across mathematics.